This paper develops and verifies a streaming method for continuously clustering the helicopter turboshaft engine's gas temperature in front of the compressor turbine short-term fluctuations to assess the initial stages of the first-stage turbine blade degradation connected to the compressor. The developed method includes a signal quality control and imputation module, adaptive baseline detrending, local robust normalization, multifunctional feature extraction in sliding windows, online dimensionality reduction, and incremental clustering with exponential “forgetting” and dynamic component lifecycle management. An expert-calibrated “cluster → physical degradation signature” map and an aggregated scalar metric based on the assignments' sliding fraction to a defective cluster are introduced for prompt alerting. The method assesses the first-stage turbine blades' degradations' initial stages connected to the compressor. The developed method was validated using TV3-117 engine flight data (1280 samples at 4 Hz) and simulated scenarios (drift, transient spikes, increased noise, flatline, and regime change). Based on the experimental results, a reproducible “defective” cluster signature was identified (increased window average and increased short-term variability). The defective assignments' sliding fraction consistently exceeded the 0.20 empirical threshold in the degradation models, ensuring early and interpretable warnings with a controlled false alarm rate.
It is known that helicopter turboshaft engines (TE) place high demands on the reliability and accuracy of operating parameter monitoring, since the compressor and compressor turbine component degradation directly affect thrust, fuel efficiency, and flight safety [1–3]. One of the most informative indicators of engine condition is the gas temperature in front of the compressor turbine, since its dynamics reflect changes in combustion modes, the blade’s aerodynamic efficiency loss, and the possible formation of localized overheating [4–6]. Modern onboard sensors record the temperature value every 2 seconds (sampling frequency of 0.5 Hz), which provides sufficient resolution to capture short-term fluctuations accompanying the degradations’ initial stages but simultaneously creates a non-stationary and noisy time series large enough to require special analysis methods [7, 8].
Traditional diagnostic approaches, such as [9, 10], often rely on thresholds, averaged values, or periodic inspections, which hinders the early detection of slowly progressing defects and lowamplitude anomalies manifested as short-term spikes or variable patterns. A flight mode instability, the external conditions' influence, and the annotated data's lack of real failures make the task particularly challenging. Methods with rigid model binding are either too sensitive to noise or lose information content with frequent mode changes [11, 12]. In such conditions, a continuous, onlineoriented algorithm capable of identifying repetitive and rare patterns in streaming two-second data appears to be a promising tool for increasing diagnostic sensitivity.
Based on the above, a method for continuous clustering of helicopter TE’s short-term gas temperature fluctuations in front of the compressor turbine development is aimed at generating robust, adaptive feature representations and cluster evolution metrics that link pattern distribution changes to the compressor and turbine components’ physical degradation. The proposed approach ensures early detection of deviations without the need for extensive tagging, increases resilience to noise and temporal non-stationarity, and enables a transition from reactive to predictive maintenance. Furthermore, it is noted that the research practical significance lies in the potential reduction in operating costs and improved flight safety through the timely identification of the compressor turbine blade degradation’s’ initial stages, thereby optimizing maintenance intervals.
The importance of monitoring the gas temperature in front of the compressor turbine for helicopter TE diagnostics has long been recognized, since its dynamics closely correlate with changes in the gas-air tract (compressor performance, combustion efficiency, local overheating) and it is often used as a key engine parameter [13]. This is the basis for both classical approaches to detecting degradation (EGT margin, basic predictive models) [14–17] and modern data-driven solutions [18–20].
Currently, there are three main areas of diagnostic approaches, which include thermodynamic methods, such as [21, 22], and threshold algorithms, such as [23, 24], and statistical and machine learning models used to construct a gas temperature values “baseline” and detect deviations. Among them, popular ones are regression methods [25, 26], autoencoders [27, 28], decision trees [29, 30], and boosting methods [31, 32], as well as complex digital twins [33] and deep neural network architectures, including LSTM [34, 35], Transformer models [36, 37], and hybrid solutions, such as [38–40], used to predict degradation and estimate the remaining service life. Recent studies demonstrate the significant potential of digital twins and deep neural networks for accurately modeling degradation processes. At the same time, these methods place increased demands on the correct normalization of data and accounting for changes in operating modes.
One of the main challenges is the temporal variability of operating conditions (flight mode changes, load changes, external conditions) and the low-amplitude presence, short-term bursts in gas temperature, which traditional averaging methods and threshold detectors either ignore or mistake for noise. Recent studies, such as [41–43], highlight the need for methods that are robust to time-varying conditions. For example, spectral equalization normalization and self-tuning preprocessing improve the neural networks training under changing conditions, but do not fully solve the problem of identifying short, repeating patterns in data streams.
It is noted that in recent years, studies have appeared that use cluster analysis [44] and matrix profile-based methods [45] to detect anomalies and recurring patterns in time series (including cluster-aware modifications). These approaches are good for detecting typical patterns and local anomalies without explicit labeling; however, most implementations are designed for batch processing or focused on relatively long signal fragments (vibrations, power), rather than streaming (online) processing of gas temperatures’ high-frequency short bursts with a 0.5 Hz frequency. Furthermore, cluster-oriented matrix profile solutions rarely directly link cluster evolution to the physical degradation of the helicopter TE compressor turbine blade.
Some recent studies, such as [46], propose adaptive neural network and hybrid methods for local problems (signal reconstruction, adaptive predictive filtering), but empirical studies focusing specifically on continuous clustering of two-second gas temperature flows and their interpretation in helicopter TE compressor turbine blade degradation terms bremain insufficient. Furthermore, measurement reliability issues (dual thermocouples, data gaps, signal reconstruction) under helicopter flight conditions complicate the application of purely algorithmic solutions.
Thus, based on the above, a number of key unresolved issues have emerged, justifying the need to develop a method for continuous clustering of gas temperature short-term fluctuations in helicopter TE. Key among these is the need for reliable detection and stable extraction of lowamplitude, short-term patterns amid significant fluctuations in operating conditions. Furthermore, existing studies lack mechanisms for online adaptation to operating mode changes without requiring full retrainability of models. Furthermore, it is necessary to consider the onboard platform’s computational limitations, including limited resources and latency requirements, which dictate the requirements for the solution’s computational efficiency. Finally, with a limited number of labeled failure examples, semi- and unsupervised validation approaches are needed to assess the cluster shift's significance for substantiating technical maintenance decisions.
Therefore, each of these issues cannot be addressed using existing batch, supervised, or “basic” clustering approaches without specially developed online clustering mechanisms, adaptive normalization, a cluster evolution tracking mechanism, and procedures for linking cluster changes to physical degradation models. Therefore, developing a continuous clustering method focused on helicopter TE two-second temperature flows for assessing compressor turbine blade degradation is a pressing scientific and practical challenge.
The proposed method for continuous clustering of helicopter TE short-term temperature fluctuations in front of the compressor turbine is formalized as a dataflow algorithm that accepts as input a scalar time series of measurements xn = x(tn), where tn = t0 + 2 · n with a sampling step of Δt = 2 seconds. A window of m samples (window time Tw = 2 · m seconds) and a sliding step s (in samples) are introduced. Data flow processing is defined by the operationSn = {xn – m + 1, …, xn}. Primary preprocessing is reduced to baseline reconstruction and slow-time component suppression, within which the baseline is estimated by an exponential moving average bn=α ⋅xn+(1−α )⋅bn−1 and subtract it, obtaining the detrended signal ~xn=xn−bn . To ensure robustness to outliers, robust normalization based on the median and MAD is used [47, 48]: medn=median ( Sn) ,
MADn=median (|x – medn|) , zn= xn−medn MADn+ϵ .
(
When data is missing, local imputation is applied, which is a linear interpolation or a model
regressor. When detecting “sticking” or artifacts, a zero-variance check is introduced for the
window. That is, if Var(Sn) < δ, the signal is flagged as suspected sensor failure and reconstructed
by approximating the previous adequate windows. Each window Sn is mapped into a feature space
ℝd with a feature set combining statistics, differential, and spectral characteristics. A typical feature
vector is represented as:
ϕ ( Sn)=[ μn , σ 2n , γ n , κn , max ( Sn) , min ( Sn) , ,
d xn d2 x
dt d t 2
n , cvsf ],
(
.
∑ π k ,t−1 ∙ N ( ϕt|μk ,t−1 , Σk ,t−1)
k=1
The parameter update is performed with exponential forgetting λ ∈ (
N j ,t= λ ∙ N j ,t−1+r j ,t , μ j ,t= λ ∙ N j ,t−1 ∙ μ j ,t−1+r j ,t ∙ ϕt ,
N j ,t Σ j ,t=
⊤ λ ∙ N j ,t−1 ∙ Σ j ,t−1+r j ,t ∙ ( ϕt− μ j ,t ) ∙ ( ϕt− μ j ,t ) + ε ∙ I .
N j ,t π j ,t=
N j ,t . where μn= m1 ∙ i∑=m1 xn−m+i , σ2n
is the dispersion, γn, κn are the asymmetry and excess coefficients, ddxtn and dd2tx2n average values, cvsf is the continuous wavelet transform scale coefficients vector.
The cluster core is implemented as an incremental mixture of K components with parameters .
For assignment and updating, a stochastic gradient is used to maximize the Gaussian mixtures’
partial likelihood [49]. At the feature input step ϕt, prior weights and responsibilities are calculated
as:
are the gas temperature first and second derivatives over time
(
k
The proposed mechanism ensures adaptation to the feature distribution’s evolution and the old pattern’s forgetting. For non-degenerate distributions and automatic addition (or removal), the component is supplemented with procedures for creating new clusters under low density conditions: max N ( ϕt|μ j ,t−1 , Σ j ,t )< τ new .
j A new component is created with initial parameters
μnew=ϕt , Σnew=σ 2n ∙ I , N new= N 0 , d j ( ϕt )< √( ϕt− μ j ,t )⊤ ∙ Σ −j,1t ∙ ( ϕt− μ j ,t ) .
weak components are removed when Nj,t < τdel. To reduce the sensitivity to the distribution’s shape, it is permissible to use the density distance based on the Mahalanobis distance [50]:
The anomalousness and associated degradation score are formulated as a hybrid score that takes into account the distance from the nearest cluster, local density, and the change in cluster occupancy rates over time. The anomalous score is defined as:
A ( ϕt )=min (d j ( ϕt )) ∙ exp (− β ∙ log ( π j ,t + ε )) , (10)
j where β > 0 scales the density contribution. To aggregate trends, a cluster share aggregation window is introduced or, in discrete form,
P j ( τ )= 1 t
∙ ∫ l {assign ( ϕs)= j }ds ,
T t−τ P j ,t= 1 ∙ ∑t l {arg max (rk ,i)= j }.
W i=t−W +1 k
In the cluster evolution metric D (drift), the divergence between distributions in two adjacent intervals is used:
D (t1 , t 2)= KL( pΘ(t1)‖pΘ(t2) )= ∑j=K1 π j ,t1 ∙ log( ππ jj ,,tt21 )+ 12 × × ∑ (tr ( Σ −j,1t2 ∙ Σ j ,t1)+( μ j ,t2−μ j ,t1)⊤ ∙ Σ −j,1t2 ∙ ( μ j ,t2−μ j ,t1)−d ) . (13) j
Degradation measurement is formalized through an expertly calibrated map of clusters and physical condition. This is accomplished by introducing a “degradation signature” vector ψj for the j-th cluster, defined by statistical features (e.g., highμ value, increased σ value, spectral energy shift to the high-frequency range), and an aggregated degradation assessment
K G (t )=∑ ω j ∙ ∆ P j (t ) ∙ ⟨ ψ j , 1⟩+ γ ∙ ∆ μh ot (t ) , (14)
j=1 where ΔPj(t) = Pj,t − Pj,t-τ, ωj are the weights determined by calibration (regression or Bayesian approximation) and Δμhot is the change in the mean in “hot” clusters. In the reference degradation labels presence, it is possible to estimate the regression model s (t )≈β τ⋅Φ (T ) , β =arg min ∑ l ( s (t ) , β⊤ ∙ Φ (t ))+ λ ∙‖β‖22 , (15) β t where Φ(t) is the aggregated cluster features set, and ℓ is the loss function (e.g., quadratic). It is noted that the method is robust to noise due to several design features: 1. Robust normalization and detrending eliminate low-frequency noise. 2. Including scaling coefficients and wavelet energies in the feature space facilitates the shortterm spikes separation from background fluctuations. 3. Exponential forgetting λ allows the algorithm to adapt to long-term mode changes without retraining. 4. The procedures for creating or removing components provide mode ”memory” and automatic adjustment of the clusters’ number.
To detect sensor failures, smoothness and autocorrelation statistics are additionally calculated based on the condition that if ACF (Sn, 1) ≈ 1 and σ2n is close to zero, the window is marked as suspicious and excluded from the contributions Pj,t until the signal quality is confirmed.
The sensitivity and convergence analytical assessment is based on the fact that for a streaming gas temperature signal with a fine step η, the parameter estimates satisfy a stochastic approximation to the mixture maximum likelihood, assuming stationarity of the local interval. It is also noted that the adaptation rate is determined by λ and the effective samples’ generalized size
N eff = 1−1 λ . (16)
The computational complexity estimate per incoming milestone is based on computing the densities for all K components, which requires O(K · d2) for storing and inverting covariances (or O(K · d) for diagonal approximation of Σj). Memory is then limited to O(K · d2). Practical recommendations include choosing d ≪ m via feature selection or streaming PCA (online Oja [51]), where the principal component update is given by Oja’s rule: ωt+1=ωt +ηt ∙(ϕt−ωt ∙ (ω⊤t ∙ ϕt )) . (17)
The developed methods’ validation involves modeling the gas temperature values’ degradation (with a linear or exponential shift of the mean and an increase in variance), injecting short-term anomalies, and validating on historical flight data with expert labeling. Evaluation metrics include detection (average detection delay ∆), precision and recall, ROC-AUC for A(ϕ) rates, and the cluster structure (Silhouette, Adjusted Rand Index [52–54]) stability in the labeled intervals presence.
Thus, based on the above, Table 1 presents an algorithm for continuous clustering of short-term fluctuations in the helicopter TE gas temperature, including successive stages of streaming data reception, quality control and signal recovery, adaptive detrending and robust normalization, a window representation formation and a multifunctional feature extraction, online dimensionality reduction, incremental clustering with cluster life cycle management, the anomaly scoring calculation and the cluster structure evolution, as well as procedures for matching cluster signatures with physical signs of degradation and regulating alerts for assessing the turbine and compressor blades' condition.
Cluster lifecycle management
Tracking assignment distributions, parameter drift, and stability metrics over time. alibration and maintenance of a “cluster-physical degradation signature” correspondence map for interpretation.
(detection delay, precision, recall, cluster stability) and report generation for maintenance regulation.
Thus, a streaming method for the short-term fluctuations’ continuous clustering in the helicopter TE gas temperature in front of the compressor turbines with a 0.5 Hz sampling frequency is proposed. This method includes robust preprocessing and detrending, multifunctional feature extraction, online dimensionality reduction, and incremental clustering with cluster lifecycle management for adaptation to operating mode transitions. The method provides a scalar anomaly estimate and an aggregated degradation metric, coupled with an expertly calibrated “cluster → physical signature” map, enabling early detection of turbine and compressor blade wear signs under limited onboard computing resources.
In this study, a numerical experiment was conducted using the developed method on the helicopter TE thermal dynamics under nominal conditions. The gas temperature in front of the compressor turbine TG(t), a real measurement series of the TV3-117 engine recorded by a standard onboard sensor on a production Mi-8MTV helicopter (Figure 1), was used. The sensor is a set of 14 dual chrome-alumel thermocouples of the T-102 type [55–57]. It is noted that the tests were carried out at the 2500-meter altitude under standard atmospheric conditions (air temperature ≈ 268 K, pressure ≈ 74 kPa). Signals were recorded at the Δt = 0.25 second interval (sampling frequency 4 Hz) for 320 seconds, which provided a 1280 readings sample.
Gas temperature dynamics 1120 K , e r u t a r ep1115 m e T s a G 11100
It is noted that Figure 1 shows a TV3-117 engine’s gas temperatures in front of the compressor turbine time series with a 4 Hz sampling rate over a 0 to 320 seconds’ range. The series’ average temperature is approximately 1115 K, with measurements ranging from approximately 1090 to 1140 K. Against a weak low-frequency modulating trend background, a distinct high-frequency component is present, consisting of short-term oscillations with a typical amplitude of approximately 2 K and a characteristic period of approximately 5 seconds, manifested as regular “high-frequency” bursts.
A signal’s pre-processing was performed by the onboard controller, and a two-stage filter was used to suppress interference. This filter included initial smoothing using the Savitzky-Golay method with an 11-sample window and a third-order polynomial. Outliers were then removed using a ±3σ criterion, with gaps restored using linear interpolation. Systematic error correction took into account the thermocouples’ calibration characteristics (with an error of no more than 1.5 K) and a correction for flow velocities up to 20 m/s. Gas temperature values were also normalized to a single scale using z-normalization: z (T G)i= 2 , (18) where T (i) is the i-th gas temperatures in front of the compressor turbine value recorded by
Gmeas the helicopter’s standard sensor. Based on the above, normalized gas temperatures in front of the compressor turbine values hear were used to form the training dataset. This datasets’ fragment is presented in Table 2. ... ... ... ... ... ...
... 40,031 80,063 120,094 160,125 199,906 239,937 279,969 ... 320 1114,32 1115,25 1115,12 1115,03 1114,79 1115,22 1115,77 1114,74 ... ... ... ... ... ... ... ...
... ... ... ... ... ...
...
To assess the training datasets’ homogeneity, traditional metrics were used, including the number of observations, the mathematical expectation x and standard deviation σ, the skewness (SK) and kurtosis (KE) coefficients, the Shapiro-Wilk test (W and p-value) to check the distributions’ normality, the Augmented Dickey-Fuller (Δyt) and KPSS stationarity tests, the Ljung-Box Q(h) test to identify autocorrelation, the Durbin-Watson (DW) statistic to assess the autocorrelation of residuals after detrending, the Levene test (W) to compare variances between segments, as well as segmental analysis of means and variances over equal sampling intervals [58–60]: x= 1 ∙ ∑n xi , σ =√ 1 ∙ ∑n ( xi− x )2 , SK = 1 ∙ ∑n ( xi− x )3 , KE= 1 ∙ ∑n ( xi− x )4−3 , n i=1 n i=1 n i=1 σ n i=1 σ
W =
n 2 (∑ ai ∙ x(i)) i=1 n ∑ ( xi− x )2 i=1
p , ∆ yt=α + β ∙ t + γ ∙ yt−1+∑ δi ∙ ∆ yt−i+ εi , i=1
(19) n KPSS= n12 ∙ ∑i=n1 σS^t22 , St= ∑i=t1 ε^i , DW = ∑t=2 ( et−et−1)2 , Q=n ∙ ( n+2) ∙ ∑h ^ρ2k ,
k=1 n−k k ∑ n j ∙ ( Z j •−Z j ••)2 W =( Nk −−1k )∙ j∑=k1 ∑nj ( Zij−Z j •)2 ,
j=1 i=1 where x(i) are ordered values, and the coefficients ai depend on the expected values of the order statistics of the normal distribution, test hypothesis H0: γ = 0 (a unit root presence); model yt = rt + εt, where rt is a random walk, ^ρk is the estimated autocorrelation function, Zi j=|X ij−~X j|; ~X j i s the median of the j-th group.
Table 3 presents the training dataset’s homogeneity evaluation numerical results, which include the sample size, the main moments of the distribution (mathematical expectation, standard deviation, skewness, and kurtosis coefficients), the statistical tests results for normality, stationarity, and autocorrelation (Shapiro–Wilk, ADF, KPSS, Ljung–Box, and Durbin–Watson), and the test for variances equality (Levene) with the corresponding statistics and p-values.
According to Table 3, the training set is characterized by a mean of approximately 1115,43 Kelvin and a relatively small population variance (σ ≈ 1,99 K). The skewness and kurtosis coefficients are close to zero, indicating that the distribution is close to normal. However, formal tests of normality yield conflicting results. The Shapiro-Wilk test rejects normality for the given sample (low p-value), while the distributions’ moments are nearly symmetrical, which is a typical effect of large data datasets, in which small deviations from normality become statistically significant. Stationarity tests yield mixed results, according to which the ADF indicates a unit root (stationarity) absence, while the KPSS detects a possible deviation from stationarity, indicating the presence of a weak low-frequency trend or structural drift requiring detrending. The Durbin-Watson statistic low value and the significant Ljung-Box test indicate a pronounced autocorrelation in the series. At the same time, the Levene test does not reveal statistically significant differences in variances between quartile segments, which confirms the relative homogeneity of the variance component over time.
In addition, Table 4 presents the dataset segmental analysis results across four equal intervals, namely, each segment’s readings’ initial and final indices, the average gas temperature level estimated values (Mean, K), and the corresponding variances (Var, K), which allow us to estimate the series’ first and second moments’ temporal homogeneity. 1115,3
Var, K 1,702 2,049 2,084 1,799
Segment analysis (Table 4) shows that the estimated mean temperature levels in all four equal intervals are close to each other (the means spread does not exceed ≈ 0,26 K), indicating a stable baseline signal level and the absence of large-scale changes in operating modes in the observation interval under consideration. Segment variances are also within a narrow range (≈ 1,70…2,08 K2), while the observed minor increases in variability in the second and third segments indicate a local increase in short-term fluctuations rather than a systematic change in noise or a level shift. Taken together, these results confirm the time series’ first and second moments’ relative homogeneity, simultaneously emphasizing the need to apply locally adaptive normalization procedures and account for the variance of temporal variability when constructing stream clustering.
A study was conducted on continuous clustering of short-term fluctuations in exhaust gas temperature for a controlled scenarios set:
2. Increased noise level. 3. Slow average level drift. 4. Transient spikes. 5. Sensor “flatline” artifacts. 6. Regime change.
For each scenario, sliding window preprocessing, multifunctional feature extraction, streaming clustering, and cluster share evolution analysis were implemented to assess the method’s sensitivity, robustness, and early detection of degradation indicators. The studies’ results are shown in Figure 2.
The PCA projection shown in Figure 2a shows three relatively compact point clouds with partial overlap. One cluster is noted to occupy the central-lower region, while the other two are shifted to the left and upward along the PC axes. The resulting clustering structure indicates the presence of reproducible local patterns in the feature space under the nominal conditions. However, the projection shown in Figure 2b shows a noticeable expansion of the cluster clouds and an increase in overlapping zones, with one component acquiring a more extended distribution in the PC1 direction. The obtained clustering results indicate a decrease in cluster separability with increasing noise levels. The resulting clustering projection shown in Figure 2c demonstrates a cluster’s shift and partial separation along the PC axes. It is also noted that the clouds are partially located along the directional gradient of PC1, which is consistent with a slow trend presence in the features. The obtained results indicate that gradual changes in the mode manifest themselves as smooth motion in the feature space and can be detected by monitoring centroids or drift metrics. Figure 2d clearly shows individual outliers and distinct groups separated from the main body of observations. It is noted that these outliers form distinct clusters or tail branches in the projection. This behavior confirms the feature set's ability to identify short-term, high-amplitude events but also highlights the false-positive risk interpretations without additional aggregation logic based on duration and frequency of events. The PCA projection shown in Figure 2e contains a “compact dense cloud” corresponding to background variability and a separate compact cluster, which is a set of points separated in the feature space. The resulting cluster separation is consistent with the sensor’s “sticking” period. It is noted that this distribution requires the diagnostic signal quality criteria to be used to distinguish true physical modes from measurement artifacts and to exclude artifactual clusters from the training set. The projection shown in Figure 2f reveals two adjacent but distinct regions, one of which contains dense clusters, while the other contains points shifted along PC1, which correlates with the modeled mean shift. The resulting cluster topology indicates the possibility of detecting mode changes based on distribution changes in the feature space and justifies the use of thresholds for changes in cluster proportions or centroid shift monitoring for rapid alerting.
a d f
Based on the gas temperature in front of the compressor turbine parameter clustering, corresponding diagrams were obtained, which show characteristic patterns associated with a defect in the compressor turbine blades (Figure 3).
Thus, as a result of the developed continuous clustering method’s experimental implementations, a defect detection in a first-stage turbine blade directly related to the compressor drive (the first turbine stage blade driving the compressor) is accomplished by identifying persistent or repeating assignments of sliding window feature vectors to a single cluster. This “defective” cluster’s centroid is characterized by an elevated average window temperature and increased short-term variability, which corresponds to the physical mechanisms of localized overheating. In this context, the proposed defect types include fatigue or impact cracks in the leading edge and root joint, the working surfaces’ erosive abrasion, and the protective coatings’ localized loss (coating spallation), as well as an increase in the gap between the blade tip and the guide vanes due to wear. All of these defects lead to the heat transfers’ localized deterioration and the short-term “hot” events formation in the TG field. In feature space, this manifests as a separate, partially distant point cloud in the PCA projection, while in the time domain, it manifests as a short-term spike’s series and a subsequent increase in the assignments proportion to the “defective” cluster. For operational detection, a scalar indicator representing an assignment’s sliding proportion to the defective cluster was used, with a 0.20 empirical threshold. Exceeding this threshold over a certain number of sliding steps is considered a warning trigger. The proposed approach provides a balance between sensitivity and robustness to single outliers but requires explicitly adjusting the threshold based on historical degradation markers and accounting for the detection time delay due to the window length and aggregation step. It has been analytically shown that individual short-term spikes can generate false positives without additional logic for aggregation by frequency and duration of events, and a shift in the operating mode (drift or regime change) generates a centroids’ smooth movement in the feature space, which requires the detrending [61] or exponential “forgetting” [62] use during the cluster’s online updating.
Time series with detected defect windows highlighted
K1125 , e r tu1120 a r e p1115 m e T1110 s a G1105 1100 3 2 1 2 C0 P -1 -2 -3 0 50 100 200 250 300 PCA projection of sliding-window features (defect cluster highlighted)
Cluster #2 Cluster #3 -2 0 4 6
A comparative analysis (Table 5) shows that the developed streaming continuous clustering method occupies a practical niche between simple physical threshold approaches and resourceintensive deep learning models. The developed methods’ application provides high potential for early detection of short-term patterns while being operationally compatible with online processing, while requiring minimal labeling and moderate computational costs.
According to Table 5, the developed method’s advantages over its closest analogues include adaptability to mode drift and interpretability through matching cluster signatures with physical degradation markers. These advantages are offset by moderate robustness to high noise levels and the need for signal quality control modules. It is noted that traditional threshold schemes are simple and interpretable but ineffective for short-term events. Deep models demonstrate high accuracy with large labeled datasets but are inapplicable to resource-constrained onboard electronics without significant optimization.
Based on the above, the practical recommendation is to use streaming clustering as an operational screening method, followed by verification through physical and statistical tests. In the labeled precedents’ presence, it is necessary to use a retrospective confirmation model (DNN, digital twin [62–65]) to improve accuracy and reduce the false positive proportion.
It is also noted that the developed methods’ practical limitations are related to the features and the clustering algorithm selected sets’ sensitivity to the noise level and sensor artifacts (flatlines, sticking, etc.). Therefore, its implementation should include signal quality control procedures (dispersion and autocorrelation checks, flatline detection) and a cluster verification module using physically interpretable indicators (temperature markers, blade distribution, diagnostic measurements), as well as a calibration step on labeled degradation examples to evaluate ROC curves, select the optimal threshold, and determine the minimum warning stability time. Implementation into an onboard monitoring system requires preliminary sensitive parameter analysis (window length, step size, number of clusters, and fraction threshold), testing on synthetic defect injections, and adaptive recalibration procedure development for changing operating modes, taking into account computational limitations and latency requirements.
Thus, the streaming clustering with cluster lifecycle management and a physically based “cluster → defect” map combination is an important technical contribution, enabling early, robust, and interpretable detection of the helicopter TE compressor turbine blades degradations’ initial stages within the onboard computing platforms’ limitations.
A streaming method for continuous clustering of short-term gas temperature in front of the compressor turbine fluctuations of helicopter turboshaft engines has been developed, focused on streaming two-second measurements. The developed method consists of a processing pipeline. There are quality control and imputation, adaptive baseline detrending, robust local normalization, sliding window generation, multifunctional feature extraction (statistical moments, difference characteristics, short-term spectral-wavelet components), streaming dimensionality reduction, and incremental clustering with exponential “forgetting” and dynamic component lifecycle management. To translate statistical inferences into diagnostic solutions, an expert-calibrated “cluster ↔ physical degradation signature” map and an aggregated scalar degradation metric based on changes in the cluster assignments proportions are proposed. The developed method introduces several modification elements to ensure a balance between sensitivity to short-term patterns and robustness to single outliers: 1. A robust detrending and local MAD normalization integration for robustness to regime shifts. 2. A streaming clustering scheme with dynamic component creation or deletion mechanisms and exponential forgetting, ensuring adaptation to regime shift without batch retraining. 3. A combined anomaly score that takes into account the distance to the cluster centroid, cluster density, and cluster population rate variations. 4. Aggregation logic based on the assignment’s sliding proportion to a defective cluster to reduce the number of false positives.
The developed method was validated using a real set of TV3-117 engine compressor turbine gas temperature measurements (Mi-8MTV flight recordings, 1280 samples at 4 Hz after preprocessing) and simulated scenarios, such as nominal mode, increased noise, slow drift, transient spikes, flatline artifacts, and mode transitions. The experiment revealed a reproducible “cluster” signature associated with the first-stage rotor blade degradations’ initial stage. A defective cluster’s centroid is characterized by an elevated average window temperature and increased short-term variability, forming a partially distant cloud in the PCA projection, while in the time domain, a short-term “hot” spike series and an increase in the assignments proportion are formed. The practical detection trigger is implemented as the defective assignments’ sliding proportion excess above a 0.20 empirical threshold over a minimum number of windows. This criterion’s introduction demonstrated the developed methods’ ability to detect degradation departments earlier than traditional packet or threshold schemes, with acceptable resistance to single noise pulses.
The research was supported by the Ministry of Internal Affairs of Ukraine “Theoretical and applied aspects of the development of the aviation sphere” under Project No. 0123U104884.
During this study preparation, the authors used ChatGPT-4.0, Gemini 2.5 flash, Grammarly to
correct and improve the text quality, and also to eliminate grammatical errors. The authors have
reviewed and edited the output and take full responsibility for this publications’ content.
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